Markov chain Monte Carlo (MCMC) is a standard technique to sample from a target distribution by simulating Markov chains. In an analogous fashion to MCMC, this paper proposes a deterministic sampling algorithm based on deterministic random walk, such as the rotor-router model (a.k.a. Propp machine). For the algorithm, we give an upper bound of the point-wise distance (i.e., infinity norm) between the "distributions" of a deterministic random walk and its corresponding Markov chain in terms of the mixing time of the Markov chain. As a result, for uniform sampling of #P-complete problems, such as 0-1 knapsack solutions, linear extensions, matchings, etc., for which rapidly mixing chains are known, our deterministic algorithm provides samples with a "distribution" with a point-wise distance at most ε from the target distribution, in time polynomial in the input size and ε-1. © 2014 Springer International Publishing Switzerland.
CITATION STYLE
Shiraga, T., Yamauchi, Y., Kijima, S., & Yamashita, M. (2014). L∞-Discrepancy analysis of polynomial-time deterministic samplers emulating rapidly mixing chains. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 8591 LNCS, pp. 25–36). Springer Verlag. https://doi.org/10.1007/978-3-319-08783-2_3
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